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首页> 外文期刊>Journal of the Mathematical Society of Japan >Remarks on surfaces with c_1~2 = 2x-1 having non-trivial 2-torsion Dedicated to Professor Fabrizio Catanese on the occasion of his 60th birthday
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Remarks on surfaces with c_1~2 = 2x-1 having non-trivial 2-torsion Dedicated to Professor Fabrizio Catanese on the occasion of his 60th birthday

机译：c_1〜2 = 2x-1且具有非平凡2扭转的曲面上的备注专门献给Fabrizio Catanese教授60岁生日

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We shall show that any complex minimal surface of general type with c_1~2 = 2x -1 having non-trivial 2-torsion divisors, where c_1~2 and x are the first Chern number of a surface and the Euler characteristic of the structure sheaf respectively, has the Euler characteristic x not exceeding 4. Moreover, we shall give a complete description for the surfaces of the case x = 4, and prove that the coarse moduli space for surfaces of this case is a unirational variety of dimension 29. Using the description, we shall also prove that our surfaces of the case x = 4 have non-birational bicanonical maps and no pencil of curves of genus 2, hence being of so called non-standard case for the non-birationality of the bicanonical maps.
机译：我们将证明c_1〜2 = 2x -1的具有通用类型的任何复杂最小曲面具有非平凡的2扭除数，其中c_1〜2和x是表面的第一Chern数和结构层的欧拉特性分别具有不超过4的欧拉特性x。而且，我们将对x = 4的情况的表面给出完整的描述，并证明该情况下的表面的粗模空间是尺寸29的非理性变化。在描述中，我们还将证明x = 4的情况的曲面具有非二元双正典图，并且没有属2的曲线笔，因此对于双正典图的非二元性而言，这就是所谓的非标准情况。

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